Fermions from classical statistics

Journal Article · Wed Dec 15 04:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.07.003· OSTI ID:21452972

Wetterich, C ^[1]

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1. Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)

We describe fermions in terms of a classical statistical ensemble. The states {tau} of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p{sub {tau}} amounts to a rotation of the wave function q{sub {tau}}(t)={+-}{radical}(p{sub {tau}}(t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

• OSTI ID: 21452972
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 12 Vol. 325; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CRYSTAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
FERMIONS
FIELD THEORIES
FUNCTIONS
INTEGRALS
ISING MODEL
MATHEMATICAL MODELS
MATHEMATICS
MOTION
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTUM FIELD THEORY
QUANTUM STATES
ROTATION
SCHROEDINGER EQUATION
STATISTICS
WAVE EQUATIONS
WAVE FUNCTIONS